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Math Help - Verifying Identities

  1. #1
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    Verifying Identities

    Verify that the left side is equal to the right side

    \frac{1+cos 3t}{sin3t} + \frac{sin 3 t}{1+ cos 3 t} = 2 csc 3 t
    Last edited by purplec16; March 5th 2010 at 07:16 PM.
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    Quote Originally Posted by purplec16 View Post
    Verify that the left side is equal to the right side

    1+cos 3t/sin3t + sin 3 t/ 1+ cos 3 t = 2 csc 3 t
    I can't read this. Please use brackets where they're needed or else use LaTeX.


    Is it \frac{1 + \cos{3t}}{\sin{3t}} + \frac{\sin{3t}}{1 + \cos{3t}} = 2\csc{3t}?
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    Yes that is the correct reading it would not go through correctly in the latex, sorry, i fixed it
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    \frac{1 + \cos{3t}}{\sin{3t}} + \frac{\sin{3t}}{1 + \cos{3t}} = \frac{(1 + \cos{3t})^2}{\sin{3t}(1 + \cos{3t})} + \frac{\sin^2{3t}}{\sin{3t}(1 + \cos{3t})}

     = \frac{1 + 2\cos{3t} + \cos^2{3t} + \sin^2{3t}}{\sin{3t}(1 + \cos{3t})}

     = \frac{1 + 2\cos{3t} + 1}{\sin{3t}(1 + \cos{3t})}

     = \frac{2 + 2\cos{3t}}{\sin{3t}(1 + \cos{3t})}

     = \frac{2(1 + \cos{3t})}{\sin{3t}(1 + \cos{3t})}

     = \frac{2}{\sin{3t}}

     = 2\csc{3t}.
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  5. #5
    Member purplec16's Avatar
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    Can you help me with another one?
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    Quote Originally Posted by purplec16 View Post
    Can you help me with another one?
    I can if you post it...
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    In this post or another? The next one is: (sec  u- tan  u)(csc  u + 1)= cot  u
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    Quote Originally Posted by purplec16 View Post
    In this post or another? The next one is: (sec  u- tan  u)(csc  u + 1)= cot  u
    (\sec{u} - \tan{u})(\csc{u} + 1) = \sec{u}\csc{u} + \sec{u} - \csc{u}\tan{u} - \tan{u}

     = \frac{1}{\cos{u}\sin{u}} + \frac{1}{\cos{u}} - \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin{u}}{\cos{u}}

     = \frac{1 + \sin{u} - \sin{u} - \sin^2{u}}{\cos{u}\sin{u}}

     = \frac{1 - \sin^2{u}}{\cos{u}\sin{u}}

     = \frac{\cos^2{u}}{\cos{u}\sin{u}}

     = \frac{\cos{u}}{\sin{u}}

     = \cot{u}.
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  9. #9
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    I dont see how you transition from the 2nd line to the the 3rd line
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    Quote Originally Posted by purplec16 View Post
    I dont see how you transition from the 2nd line to the the 3rd line
    Get a common denominator of \cos{u}\sin{u}.
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  11. #11
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    I get it never mind
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  12. #12
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    Quote Originally Posted by purplec16 View Post
    I understand that part, I dont understand how you got the numerator
    \frac{1}{\cos{u}\sin{u}} + \frac{1}{\cos{u}} - \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin{u}}{\cos{u}}

     = \frac{1}{\cos{u}\sin{u}} + \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin{u}}{\cos{u}\sin{u}} - \frac{\sin^2{u}}{\cos{u}\sin{u}}

    = \frac{1 + \sin{u} - \sin{u} - \sin^2{u}}{\cos{u}\sin{u}}<br />
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  13. #13
    Member purplec16's Avatar
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    Thank You so much, I understand
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  14. #14
    Member purplec16's Avatar
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    Can you help me with one more please?
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  15. #15
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    Quote Originally Posted by purplec16 View Post
    Can you help me with one more please?
    Go on... Since I've given you two full solutions though, I'd like to see your attempt at proving it this time...
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